%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC316+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:53 AM UTC 2025
% Result : Theorem 0.87s 1.07s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC316+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 08:58:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.87/1.07 % SZS status Theorem
% 0.87/1.07 % SZS output start Proof
% 0.87/1.07 tff(tptp_fun_V_46_type, type, (
% 0.87/1.07 tptp_fun_V_46: $i)).
% 0.87/1.07 tff(app_type, type, (
% 0.87/1.07 app: ( $i * $i ) > $i)).
% 0.87/1.07 tff(cons_type, type, (
% 0.87/1.07 cons: ( $i * $i ) > $i)).
% 0.87/1.07 tff(nil_type, type, (
% 0.87/1.07 nil: $i)).
% 0.87/1.07 tff(hd_type, type, (
% 0.87/1.07 hd: $i > $i)).
% 0.87/1.07 tff(tptp_fun_U_45_type, type, (
% 0.87/1.07 tptp_fun_U_45: $i)).
% 0.87/1.07 tff(tl_type, type, (
% 0.87/1.07 tl: $i > $i)).
% 0.87/1.07 tff(tptp_fun_Y_47_type, type, (
% 0.87/1.07 tptp_fun_Y_47: $i)).
% 0.87/1.07 tff(tptp_fun_Z_48_type, type, (
% 0.87/1.07 tptp_fun_Z_48: $i)).
% 0.87/1.07 tff(ssList_type, type, (
% 0.87/1.07 ssList: $i > $o)).
% 0.87/1.07 tff(ssItem_type, type, (
% 0.87/1.07 ssItem: $i > $o)).
% 0.87/1.07 tff(neq_type, type, (
% 0.87/1.07 neq: ( $i * $i ) > $o)).
% 0.87/1.07 tff(1,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2,plain,
% 0.87/1.07 ((ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(3,plain,
% 0.87/1.07 ((~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))) <=> (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(4,plain,
% 0.87/1.07 ((ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))) <=> (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[3])).
% 0.87/1.07 tff(5,plain,
% 0.87/1.07 ((ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[4])).
% 0.87/1.07 tff(6,plain,
% 0.87/1.07 ((ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[5, 2])).
% 0.87/1.07 tff(7,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[6])).
% 0.87/1.07 tff(8,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[7, 1])).
% 0.87/1.07 tff(9,plain,
% 0.87/1.07 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(10,plain,
% 0.87/1.07 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)))))) | (?[X1: $i] : ((ssList(X1) & (V = X1)) & ?[X2: $i] : (ssList(X2) & ?[X3: $i] : ((((ssList(X3) & (tl(U) = X2)) & (app(X2, X3) = X1)) & ?[X4: $i] : (((ssItem(X4) & (cons(X4, nil) = X3)) & (hd(U) = X4)) & neq(nil, U))) & neq(nil, U)))) & neq(U, nil))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(app(cons(Y, nil), Z) = W)) | (~(app(Z, cons(Y, nil)) = X)))))) | (?[X1: $i] : ((ssList(X1) & (V = X1)) & ?[X2: $i] : (ssList(X2) & ?[X3: $i] : ((((ssList(X3) & (tl(U) = X2)) & (app(X2, X3) = X1)) & ?[X4: $i] : (((ssItem(X4) & (cons(X4, nil) = X3)) & (hd(U) = X4)) & neq(nil, U))) & neq(nil, U)))) & neq(U, nil))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.87/1.07 tff(12,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.87/1.07 tff(13,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.87/1.07 tff(14,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.87/1.07 tff(15,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(nil, U) & ssList(V) & ssItem(hd(U)) & ssList(tl(U)) & ssList(cons(hd(U), nil)) & (app(tl(U), cons(hd(U), nil)) = V) & neq(U, nil)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(app(cons(Y, nil), Z) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.87/1.07 tff(16,plain,
% 0.87/1.07 (ssList(U!45) & ssList(V!46) & (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.87/1.07 tff(17,plain,
% 0.87/1.07 (~((~ssList(Z!48)) | (~(app(cons(Y!47, nil), Z!48) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))),
% 0.87/1.07 inference(and_elim,[status(thm)],[16])).
% 0.87/1.07 tff(18,plain,
% 0.87/1.07 (app(Z!48, cons(Y!47, nil)) = V!46),
% 0.87/1.07 inference(or_elim,[status(thm)],[17])).
% 0.87/1.07 tff(19,plain,
% 0.87/1.07 (ssList(Z!48)),
% 0.87/1.07 inference(or_elim,[status(thm)],[17])).
% 0.87/1.07 tff(20,plain,
% 0.87/1.07 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(21,plain,
% 0.87/1.07 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[20])).
% 0.87/1.07 tff(22,plain,
% 0.87/1.07 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(23,plain,
% 0.87/1.07 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[22])).
% 0.87/1.07 tff(24,plain,
% 0.87/1.07 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[23, 21])).
% 0.87/1.07 tff(25,plain,
% 0.87/1.07 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(26,plain,
% 0.87/1.07 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (hd(cons(V, U)) = V)) <=> ((~ssItem(V)) | (hd(cons(V, U)) = V)))), (![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)) <=> ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(27,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[26])).
% 0.92/1.08 tff(28,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax23')).
% 0.92/1.08 tff(29,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.92/1.08 tff(30,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.92/1.08 tff(31,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[30])).
% 0.92/1.08 tff(32,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.92/1.08 tff(33,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(34,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(35,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.92/1.08 tff(36,plain,
% 0.92/1.08 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.92/1.08 tff(37,plain,
% 0.92/1.08 (ssItem(Y!47)),
% 0.92/1.08 inference(and_elim,[status(thm)],[16])).
% 0.92/1.08 tff(38,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))) | ((~ssItem(Y!47)) | (hd(cons(Y!47, Z!48)) = Y!47))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))) | (~ssItem(Y!47)) | (hd(cons(Y!47, Z!48)) = Y!47))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(39,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))) | ((~ssItem(Y!47)) | (hd(cons(Y!47, Z!48)) = Y!47))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(40,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, Z!48)) = V))) | (~ssItem(Y!47)) | (hd(cons(Y!47, Z!48)) = Y!47)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.92/1.08 tff(41,plain,
% 0.92/1.08 (hd(cons(Y!47, Z!48)) = Y!47),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[40, 37, 36])).
% 0.92/1.08 tff(42,plain,
% 0.92/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(43,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[42])).
% 0.92/1.08 tff(44,plain,
% 0.92/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(45,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[44])).
% 0.92/1.08 tff(46,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[45, 43])).
% 0.92/1.08 tff(47,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(48,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(49,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[48])).
% 0.92/1.08 tff(50,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax81')).
% 0.92/1.08 tff(51,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.92/1.08 tff(52,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.92/1.08 tff(53,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(skolemize,[status(sab)],[52])).
% 0.92/1.08 tff(54,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.92/1.08 tff(55,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(56,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(57,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.92/1.08 tff(58,plain,
% 0.92/1.08 (![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[57, 54, 19])).
% 0.92/1.08 tff(59,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))) | ((~ssItem(Y!47)) | (cons(Y!47, Z!48) = app(cons(Y!47, nil), Z!48)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))) | (~ssItem(Y!47)) | (cons(Y!47, Z!48) = app(cons(Y!47, nil), Z!48)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(60,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))) | ((~ssItem(Y!47)) | (cons(Y!47, Z!48) = app(cons(Y!47, nil), Z!48)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(61,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (cons(V, Z!48) = app(cons(V, nil), Z!48)))) | (~ssItem(Y!47)) | (cons(Y!47, Z!48) = app(cons(Y!47, nil), Z!48))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.92/1.08 tff(62,plain,
% 0.92/1.08 (cons(Y!47, Z!48) = app(cons(Y!47, nil), Z!48)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[61, 37, 58])).
% 0.92/1.08 tff(63,plain,
% 0.92/1.08 (app(cons(Y!47, nil), Z!48) = cons(Y!47, Z!48)),
% 0.92/1.08 inference(symmetry,[status(thm)],[62])).
% 0.92/1.08 tff(64,plain,
% 0.92/1.08 (app(cons(Y!47, nil), Z!48) = U!45),
% 0.92/1.08 inference(or_elim,[status(thm)],[17])).
% 0.92/1.08 tff(65,plain,
% 0.92/1.08 (U!45 = app(cons(Y!47, nil), Z!48)),
% 0.92/1.08 inference(symmetry,[status(thm)],[64])).
% 0.92/1.08 tff(66,plain,
% 0.92/1.08 (U!45 = cons(Y!47, Z!48)),
% 0.92/1.08 inference(transitivity,[status(thm)],[65, 63])).
% 0.92/1.08 tff(67,plain,
% 0.92/1.08 (hd(U!45) = hd(cons(Y!47, Z!48))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[66])).
% 0.92/1.08 tff(68,plain,
% 0.92/1.08 (hd(U!45) = Y!47),
% 0.92/1.08 inference(transitivity,[status(thm)],[67, 41])).
% 0.92/1.08 tff(69,plain,
% 0.92/1.08 (cons(hd(U!45), nil) = cons(Y!47, nil)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[68])).
% 0.92/1.08 tff(70,plain,
% 0.92/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(71,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[70])).
% 0.92/1.08 tff(72,plain,
% 0.92/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(73,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[72])).
% 0.92/1.08 tff(74,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[73, 71])).
% 0.92/1.08 tff(75,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(76,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (tl(cons(V, U)) = U)) <=> ((~ssItem(V)) | (tl(cons(V, U)) = U)))), (![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)) <=> ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(77,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[76])).
% 0.92/1.08 tff(78,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax25')).
% 0.92/1.08 tff(79,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.92/1.08 tff(80,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.92/1.08 tff(81,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[80])).
% 0.92/1.08 tff(82,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.92/1.08 tff(83,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(84,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(85,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.92/1.08 tff(86,plain,
% 0.92/1.08 (![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[85, 82, 19])).
% 0.92/1.08 tff(87,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))) | ((~ssItem(Y!47)) | (tl(cons(Y!47, Z!48)) = Z!48))) <=> ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))) | (~ssItem(Y!47)) | (tl(cons(Y!47, Z!48)) = Z!48))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(88,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))) | ((~ssItem(Y!47)) | (tl(cons(Y!47, Z!48)) = Z!48))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(89,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, Z!48)) = Z!48))) | (~ssItem(Y!47)) | (tl(cons(Y!47, Z!48)) = Z!48)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.92/1.08 tff(90,plain,
% 0.92/1.08 (tl(cons(Y!47, Z!48)) = Z!48),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[89, 37, 86])).
% 0.92/1.08 tff(91,plain,
% 0.92/1.08 (tl(U!45) = tl(cons(Y!47, Z!48))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[66])).
% 0.92/1.08 tff(92,plain,
% 0.92/1.08 (tl(U!45) = Z!48),
% 0.92/1.08 inference(transitivity,[status(thm)],[91, 90])).
% 0.92/1.08 tff(93,plain,
% 0.92/1.08 (app(tl(U!45), cons(hd(U!45), nil)) = app(Z!48, cons(Y!47, nil))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[92, 69])).
% 0.92/1.08 tff(94,plain,
% 0.92/1.08 (app(tl(U!45), cons(hd(U!45), nil)) = V!46),
% 0.92/1.08 inference(transitivity,[status(thm)],[93, 18])).
% 0.92/1.08 tff(95,plain,
% 0.92/1.08 (ssList(cons(hd(U!45), nil)) <=> ssList(cons(Y!47, nil))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[69])).
% 0.92/1.08 tff(96,plain,
% 0.92/1.08 (ssList(cons(Y!47, nil)) <=> ssList(cons(hd(U!45), nil))),
% 0.92/1.08 inference(symmetry,[status(thm)],[95])).
% 0.92/1.08 tff(97,plain,
% 0.92/1.08 (ssList(nil) <=> ssList(nil)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(98,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.92/1.08 tff(99,plain,
% 0.92/1.08 (ssList(nil)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.92/1.08 tff(100,plain,
% 0.92/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(101,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[100])).
% 0.92/1.08 tff(102,plain,
% 0.92/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(103,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[102])).
% 0.92/1.08 tff(104,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[103, 101])).
% 0.92/1.08 tff(105,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(106,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(107,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[106])).
% 0.92/1.08 tff(108,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax16')).
% 0.92/1.08 tff(109,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.92/1.08 tff(110,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.92/1.08 tff(111,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(skolemize,[status(sab)],[110])).
% 0.92/1.08 tff(112,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.92/1.08 tff(113,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(114,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(115,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.92/1.08 tff(116,plain,
% 0.92/1.08 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[115, 112, 99])).
% 0.92/1.08 tff(117,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(Y!47)) | ssList(cons(Y!47, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(Y!47)) | ssList(cons(Y!47, nil)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(118,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(Y!47)) | ssList(cons(Y!47, nil)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(119,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(Y!47)) | ssList(cons(Y!47, nil))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.92/1.08 tff(120,plain,
% 0.92/1.08 (ssList(cons(Y!47, nil))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[119, 37, 116])).
% 0.92/1.08 tff(121,plain,
% 0.92/1.08 (ssList(cons(hd(U!45), nil))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[120, 96])).
% 0.92/1.08 tff(122,plain,
% 0.92/1.08 (ssList(tl(U!45)) <=> ssList(Z!48)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[92])).
% 0.92/1.08 tff(123,plain,
% 0.92/1.08 (ssList(Z!48) <=> ssList(tl(U!45))),
% 0.92/1.08 inference(symmetry,[status(thm)],[122])).
% 0.92/1.08 tff(124,plain,
% 0.92/1.08 (ssList(tl(U!45))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[19, 123])).
% 0.92/1.08 tff(125,plain,
% 0.92/1.08 (ssItem(hd(U!45)) <=> ssItem(Y!47)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[68])).
% 0.92/1.08 tff(126,plain,
% 0.92/1.08 (ssItem(Y!47) <=> ssItem(hd(U!45))),
% 0.92/1.08 inference(symmetry,[status(thm)],[125])).
% 0.92/1.08 tff(127,plain,
% 0.92/1.08 (ssItem(hd(U!45))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[37, 126])).
% 0.92/1.08 tff(128,plain,
% 0.92/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(129,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[128])).
% 0.92/1.08 tff(130,plain,
% 0.92/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(131,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[130])).
% 0.92/1.08 tff(132,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[131, 129])).
% 0.92/1.08 tff(133,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(134,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(135,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[134])).
% 0.92/1.08 tff(136,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.92/1.08 tff(137,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.92/1.08 tff(138,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.92/1.08 tff(139,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(skolemize,[status(sab)],[138])).
% 0.92/1.08 tff(140,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.92/1.08 tff(141,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(142,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(143,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.92/1.08 tff(144,plain,
% 0.92/1.08 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[143, 140, 99])).
% 0.92/1.08 tff(145,plain,
% 0.92/1.08 (ssList(U!45)),
% 0.92/1.08 inference(and_elim,[status(thm)],[16])).
% 0.92/1.08 tff(146,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(U!45)) | (~((nil = U!45) <=> neq(nil, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(U!45)) | (~((nil = U!45) <=> neq(nil, U!45))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(147,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(U!45)) | (~((nil = U!45) <=> neq(nil, U!45))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(148,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(U!45)) | (~((nil = U!45) <=> neq(nil, U!45)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.92/1.08 tff(149,plain,
% 0.92/1.08 (~((nil = U!45) <=> neq(nil, U!45))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[148, 145, 144])).
% 0.92/1.08 tff(150,plain,
% 0.92/1.08 (cons(Y!47, Z!48) = U!45),
% 0.92/1.08 inference(transitivity,[status(thm)],[62, 64])).
% 0.92/1.08 tff(151,plain,
% 0.92/1.08 ((nil = cons(Y!47, Z!48)) <=> (nil = U!45)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[150])).
% 0.92/1.08 tff(152,plain,
% 0.92/1.08 ((~(nil = cons(Y!47, Z!48))) <=> (~(nil = U!45))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[151])).
% 0.92/1.08 tff(153,plain,
% 0.92/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(154,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[153])).
% 0.92/1.08 tff(155,plain,
% 0.92/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(156,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[155])).
% 0.92/1.08 tff(157,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(transitivity,[status(thm)],[156, 154])).
% 0.92/1.08 tff(158,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(159,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(nil = cons(V, U)))) <=> ((~ssItem(V)) | (~(nil = cons(V, U)))))), (![V: $i] : (ssItem(V) => (~(nil = cons(V, U)))) <=> ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(nil = cons(V, U))))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(nil = cons(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(160,plain,
% 0.92/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(nil = cons(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[159])).
% 0.92/1.08 tff(161,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(nil = cons(V, U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax21')).
% 0.92/1.08 tff(162,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.92/1.08 tff(163,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.92/1.08 tff(164,plain,(
% 0.92/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(skolemize,[status(sab)],[163])).
% 0.92/1.08 tff(165,plain,
% 0.92/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.92/1.08 tff(166,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(167,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))) | ((~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48)))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(168,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, U)))))) | (~ssList(Z!48)) | ![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.92/1.08 tff(169,plain,
% 0.92/1.08 (![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[168, 165, 19])).
% 0.92/1.08 tff(170,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))) | ((~ssItem(Y!47)) | (~(nil = cons(Y!47, Z!48))))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))) | (~ssItem(Y!47)) | (~(nil = cons(Y!47, Z!48))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(171,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))) | ((~ssItem(Y!47)) | (~(nil = cons(Y!47, Z!48))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(172,plain,
% 0.92/1.08 ((~![V: $i] : ((~ssItem(V)) | (~(nil = cons(V, Z!48))))) | (~ssItem(Y!47)) | (~(nil = cons(Y!47, Z!48)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.92/1.08 tff(173,plain,
% 0.92/1.08 (~(nil = cons(Y!47, Z!48))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[172, 37, 169])).
% 0.92/1.08 tff(174,plain,
% 0.92/1.08 (~(nil = U!45)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[173, 152])).
% 0.92/1.08 tff(175,plain,
% 0.92/1.08 (((nil = U!45) <=> neq(nil, U!45)) | (nil = U!45) | neq(nil, U!45)),
% 0.92/1.08 inference(tautology,[status(thm)],[])).
% 0.92/1.08 tff(176,plain,
% 0.92/1.08 (neq(nil, U!45)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[175, 174, 149])).
% 0.92/1.08 tff(177,plain,
% 0.92/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(178,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(179,plain,
% 0.92/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.92/1.08 tff(180,plain,
% 0.92/1.08 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[179, 140, 145])).
% 0.92/1.08 tff(181,plain,
% 0.92/1.08 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(182,plain,
% 0.92/1.09 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(183,plain,
% 0.92/1.09 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.92/1.09 tff(184,plain,
% 0.92/1.09 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[183, 99, 180])).
% 0.92/1.09 tff(185,plain,
% 0.92/1.09 ((U!45 = nil) <=> (nil = U!45)),
% 0.92/1.09 inference(commutativity,[status(thm)],[])).
% 0.92/1.09 tff(186,plain,
% 0.92/1.09 ((nil = U!45) <=> (U!45 = nil)),
% 0.92/1.09 inference(symmetry,[status(thm)],[185])).
% 0.92/1.09 tff(187,plain,
% 0.92/1.09 ((nil = cons(Y!47, Z!48)) <=> (U!45 = nil)),
% 0.92/1.09 inference(transitivity,[status(thm)],[151, 186])).
% 0.92/1.09 tff(188,plain,
% 0.92/1.09 ((~(nil = cons(Y!47, Z!48))) <=> (~(U!45 = nil))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[187])).
% 0.92/1.09 tff(189,plain,
% 0.92/1.09 (~(U!45 = nil)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[173, 188])).
% 0.92/1.09 tff(190,plain,
% 0.92/1.09 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.92/1.09 inference(tautology,[status(thm)],[])).
% 0.92/1.09 tff(191,plain,
% 0.92/1.09 (neq(U!45, nil)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[190, 189, 184])).
% 0.92/1.09 tff(192,plain,
% 0.92/1.09 (ssList(V!46)),
% 0.92/1.09 inference(and_elim,[status(thm)],[16])).
% 0.92/1.09 tff(193,plain,
% 0.92/1.09 ((~(~((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46))))) <=> ((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(194,plain,
% 0.92/1.09 ((neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil)) <=> (~((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46))))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(195,plain,
% 0.92/1.09 ((~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) <=> (~(~((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46)))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[194])).
% 0.92/1.09 tff(196,plain,
% 0.92/1.09 ((~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))) <=> ((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[195, 193])).
% 0.92/1.09 tff(197,plain,
% 0.92/1.09 (~(neq(nil, U!45) & ssList(V!46) & ssItem(hd(U!45)) & ssList(tl(U!45)) & ssList(cons(hd(U!45), nil)) & (app(tl(U!45), cons(hd(U!45), nil)) = V!46) & neq(U!45, nil))),
% 0.92/1.09 inference(and_elim,[status(thm)],[16])).
% 0.92/1.09 tff(198,plain,
% 0.92/1.09 ((~ssList(V!46)) | (~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.92/1.09 tff(199,plain,
% 0.92/1.09 ((~neq(U!45, nil)) | (~neq(nil, U!45)) | (~ssItem(hd(U!45))) | (~ssList(tl(U!45))) | (~ssList(cons(hd(U!45), nil))) | (~(app(tl(U!45), cons(hd(U!45), nil)) = V!46))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[198, 192])).
% 0.92/1.09 tff(200,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[199, 191, 176, 127, 124, 121, 94])).
% 0.92/1.09 % SZS output end Proof
% 0.92/1.09 % E exiting
%------------------------------------------------------------------------------